IMO Shortlist 1987 problem 21

  Avg: 0,0
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
In an acute-angled triangle ABC the interior bisector of angle A meets BC at L and meets the circumcircle of ABC again at N. From L perpendiculars are drawn to AB and AC, with feet K and M respectively. Prove that the quadrilateral AKNM and the triangle ABC have equal areas.(IMO Problem 2)

Proposed by Soviet Union.
Izvor: Međunarodna matematička olimpijada, shortlist 1987